Lab Prep - Speed of a wave on a stretched string

Hurly

1. The problem statement, all variables and given/known data

1) Show that the expression for the mass per unit length, μ, of a wire in terms of its density and diameter is

μ = [itex]\frac{πρd^2}{4}[/itex]

2) Using equations (3) and (4) show that the expression for the error in frequency in terms of the error in length and the error in diameter of the wire is given by equation 5. Assume the error in the mass is negligible.

Δf = f(ΔL/L + Δd/d)

2. Relevant equations

(3) f = [itex]\frac{n}{2L}[/itex] [itex]\sqrt{\frac{T}{μ}}[/itex]

(4) μ = [itex]\frac{πρd^2}{4}[/itex]

3. The attempt at a solution

Mass of Wire = Vol x Density

= πV^2 ρ

or of density = 2V V^2 = [itex]\frac{d}{2}[/itex]^2

∴Mass = [itex]\frac{πd^2ρ}{4}[/itex]